Statistics Module 7: Chapter 13-14
Which of the following represents the correct scores if 1, 4, 25, and 81 are transformed using the rank-order method? a) 1, 2, 5, 9 b) 1, 4, 25, 81 c) 4, 4, 25, 25 d) 1, 2, 3, 4
1, 2, 3, 4
Which of the following represents the correct scores if 4, 25, 25, and 100 are transformed using the rank-order method? a) 2, 5, 5, 10 b) 1, 2.5, 2.5, 4 c) 1, 2, 3, 4 d) 1.5, 2, 3.5, 4
1, 2.5, 2.5, 4
The reporting of chi-square tests in research articles a) almost always includes the information needed to repeat the calculation b) has been downplayed until recently c) relies exclusively on tables d) was not emphasized in research articles until recently
Almost always includes the information needed to repeat the calculation
When the assumption of a normal curve is seriously violated, the ordinary t test a) resembles an analysis of variance b) is conducted using √t instead of t c) gives an incorrect result d) is robust
Gives an incorrect result
The item below is based on the following scenario.A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow:Observed (and Expected) Frequencies Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ2(3,N= 75) = 11.85,p< .05."What proportion of boys indicated that verbal or cyber bullying was their primary method? a) (8+6)/30 = .47 b) (7+5)/30 = .40 c) (8+6)/75 = .19 d) (7+5)/75 = .16
(7+5)/30 = .40
According to Cohen's conventions for the phi coefficient, a large effect size is a) .10 b) .15 c) .40 d) .50
.50
Which of the following represents the correct scores if 4, 25, 25, and 100 are transformed using a square-root transformation? a) 2, 5, 5, 10 b) 1, 2.5, 2.5, 4 c) 1, 2, 3, 4 d) 1.5, 2, 3.5, 4
2, 5, 5, 10
The item below is based on the following scenario. In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow: Observed (and Expected) Frequencies Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ2 (4, N = 100) = 11.73, p < .05." The percentage of the middle class respondents who were Catholic was a) 7.5/34 = 22.1% b) 5/100 = 5.0% c) 5/34 = 14.7% d) 7.5/100 = 7.5%
5/34 = 14.7%
The item below is based on the following scenario. A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow: Observed (and Expected) Frequencies Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ2 (3, N = 75) = 11.85, p < .05." Which cutoff chi-square value is appropriate for testing the null hypothesis? a) 3.841 b) 5.992 c) 7.815 d) 9.488
7.815
One indication that a population is not normally distributed is when a) a small sample drawn from the population is positively skewed b) two variables are measured at the same time c) a scale or index is used for the measured variable d) a ceiling or floor effect is present in a large sample
A ceiling or floor effect is present in a large sample
If a Results section includes a sentence stating that "comparisons...were made using the Wilcoxon rank-sum test," the type of test used was a) a rank-order test b) analysis of variance c) a computer-intensive test d) a t test for indepdent means
A rank-order test
Some statisticians have shown that instead of using the special procedures involved in rank-order tests, approximately the same results can be obtained by transforming the scores into ranks and then a) figuring a Spearman Z b) finding the mean of the scores' inverses c) applying all the usual arithmetic for figuring an ordinary parametric test, such as a t test. d) applying all the usual arithmetic for figuring a typical nonparametric test, such as a Wilcoxon signed-rank test
Applying all the usual arithmetic for figuring an ordinary parametric test, such as a t test.
For the scores 0.8, 1.1, 1.7, 1.7, 2.3, and 2.6, the shape of the distribution is __________. a) approximately normal b) positively skewed c) negatively skewed d) rectangular
Approximately normal
In a study with a 3 × 2 design, Φ and Cramer's Φ a) are equivalent b) are equivalent if Φ is divided by 2 c) are equivalent if Φ is divided by √2 d) are unrelated
Are equivalent
Data transformations are legitimate a) because no information is lost or distorted b) when performed post hoc c) because the order of scores is not altered d) when they favor a researcher's hypothesis
Because the order of scores is not altered
The values in a chi-square distribution are always greater than 0 and a) are normally distributed b) less than 1 c) can be quite large d) are negatively skewed
Can be quite large
Bootstrap tests are an example of a(n) a) computer-intensive method b) post-hoc test c) unequal distribution comparison d) marginal test
Computer-intensive method
Which calculation is necessary for figuring the chi-square statistic? a) dividing the absolute differences between observed and expected frequencies by the expected frequency in each cell b) dividing the absolute differences between observed and expected frequencies by the observed frequency in each cell c) dividing the squared differences between observed and expected frequencies by the expected frequency in each cell d) dividing the squared differences between observed and expected frequencies by the observed frequency in each cell
Dividing the squared differences between observed and expected frequencies by the expected frequency in each cell
Because the distribution of rank-order scores is known exactly, rather than being estimated, rank-order tests a) do not require estimating any population parameters b) are used in most actual studies c) are almost always preferred over square-root transformations d) require drawing additional samples
Do not require estimating any population parameters
The first step in considering a data transformation is to a) examine the transformed sample distribution b) apply the most appropriate transformation c) examine the sample data to determine the shape of the distribution d) conduct cochran's test for nonnormality
Examine the sample data to determine the shape of the distribution
A chi-square test would be appropriate for examining the relationship between a) gender (male or female) and political orientation (measured on a 5-point Likert scale) b) gender (male or female) and political orientation (conservative, liberal, or other) c) education (in years) and political orientation (measured on a 5-point Likert scale) d) education (in years) and political orientation (conservative, liberal, or other)
Gender (male or female) and political orientation (conservative, liberal, or other)
One advantage of the chi-square test over most other inferential statistical procedures is that it a) can use the comparison distribution of any other statistical procedure b) does not require as many participants c) can be easily applied to repeated-measures designs d) has minimal assumptions
Has minimal assumptions
The relative advantages of data transformations versus rank-order tests in terms of power a) have not been well established b) were well established in the 1980s c) were well established in the 1920s d) are irrelevant
Have not been well established
A sample drawn from a normally distributed population a) might have more members than the population. b) is sometimes approximately normally distributed c) is always approximately normally distributed d) is never approximately normally distributed
Is sometimes approximately normally distributed
Which of the following statements about the phi coefficient is incorrect? a) it is symbolized by the Greek letter Φ b) it ranges from 0 to 1 c) It can be interpreted in the same manner as a correlation coefficient d) It is based on the chi-square statistic and the degrees of freedom
It is based on the chi-square statistic and the degrees of freedom
The inventor of the chi-square test was a) Karl Pearson b) W. S. Gossett c) Ronald Fisher d) Francis Galton
Karl Pearson
When conducting a statistical test, a single outlier can a) make the test more robust to violations of the assumption of normality. b) reduce the sample's variance, making significant results easier to achieve c) lead to a significant result when the other members of the sample considered without the outlier would not lead to a significant result d) improve the reliability of the statistical procedure
Lead to a significant result when the other members of the sample considered without the outlier would not lead to a significant result
Having discovered an extreme score in a sample of scores, the first thing to do is to a) discard the score b) make sure the score was not recorded in error c) perform a log transformation d) perform an inverse transformation
Make sure the score was not recorded in error
Which procedure can be performed without the aid of computers? a) approximate randomization test b) Mann-Whitney U test c) bootstrap test d) randomization test
Mann-Whitney U test
In a square-root transformation, a) high numbers become lower, and low numbers become higher. b) moderate numbers remain unchanged, but low numbers become slightly higher c) low numbers become much lower, but high numbers remain basically unchanged d) moderate numbers become only slightly lower, but high numbers become much lower
Moderate numbers become only slightly lower, but high numbers become much lower
A way to determine the number of people expected to be in any one cell of a chi-square contingency table is to a) multiply the number of people for the cell's column by its row proportion, figuring its row proportion as the number of people for the cell's row divided by the total number of people b) divide the total number of people by the number of people in the cell and multiply this result by a row proportion, figuring its row proportion as the number of people for the cell's row divided by the total number of people c) multiply the number of people in the cell's row by the number of people in the cell's column d) divide the number of people in the cell's row by the number of people in the cell's column
Multiply the number of people for the cell's column by its row proportion, figuring its row proportion as the number of people for the cell's row divided by the total number of people
In a chi-square test, the variables are a) rank-order b) equal-interval c) quantitative d) nominal
Nominal
Which of the following is part of the randomization test procedure? a) ordering the difference scores from lowest to highest b) rank-ordering the scores within each group c) looking up the cutoff score or critical value in a standard table d) applying a square-root transformation
Ordering the difference scores from lowest to highest
The item below is based on the following scenario. A school psychologist surveyed 75 students (both boys and girls) who had been reported as "bullies" and asked them which bullying method they used most often: physical, verbal, psychological, or cyber-bullying. The results and an excerpt from this fictitious study follow: Observed (and Expected) Frequencies Excerpt: "Based on a chi-square test for independence, there was a significant association between gender and bullying method, χ2 (3, N = 75) = 11.85, p < .05." Which bullying method was expected to be the most common among girls? a) physical b) verbal c) psychological d) cyber
Physical
Prior to using a procedure that is "distribution-free," the sample scores would probably be transformed using the a) reflection method b) antilog method c) rank-order method d) inverse method
Rank-order method
A distribution of rank-ordered scores will always be a) a normal curve b) bimodal c) rectangular d) skewed
Rectangular
For the scores 12, 13, 14, 15, 16, and 17, the shape of the distribution is __________. a) approximately normal b) positively skewed c) negatively skewed d) rectangular
Rectangular
When a distribution is negatively skewed, which of the following transformations should be performed first? a) square-root b) log c) inverse d) reflection
Reflection
In research articles, data transformations are usually mentioned in the a) discussion section b) reference list c) participants section d) results section
Results section
In general, the t test and the analysis of variance are a) dependent on five basic assumptions b) free of assumptions c) sensitive to violations of assumptions d) robust to violations of assumptions
Robust to violations of assumptions
One unsettled controversy regarding chi-square tests has to do with a) large observed frequencies b) large expected frequencies c) small observed frequencies d) small expected frequencies
Small expected frequencies
The rank-order test that would be used in the same kind of research situation as the correlation coefficient is a) the Wilcoxon signed-rank test b) the Wilcoxon rank-sum test c) the Kruskal-Wallis H test d) Spearman's rho
Spearman's rho
Which of the following is a nonparametric test? a) analysis of variance b) t test for dependent means c) Spearman's rho d) t test for independent means
Spearman's rho
A common transformation procedure when scores are positively skewed is the a) square-root transformation b) squared transformation c) exponential transformation d) sign-reversal transformation
Square-root transformation
The main idea of a chi-square test is to a) test the estimated degree of fit (proportion of variance accounted for) of one variable to the other variable b) compare the estimated population means, to see if they vary from each other by more than chance c) compare estimated population variances, to see if they vary from each other by more than chance d) test how well the pattern of observed frequencies fits some expected pattern of frequencies
Test how well the pattern of observed frequencies fits some expected pattern of frequencies
The rank-order test that would be used in the same kind of research situation as an analysis of variance is a) the Wilcoxon signed-rank test b) the Wilcoxon rank-sum test c) the Kruskal-Wallis H test d) Spearman's rho
The Kruskal-Wallis H test
The rank-order test that would be used in the same kind of research situation as a t test for independent means is a) the Wilcoxon signed-rank test b) the Wilcoxon rank-sum test c) the Kruskal-Wallis H test d) Spearman's rho
The Wilcoxon rank-sum test
The rank-order test that would be used in the same kind of research situation as a t test for dependent means is a) the Wilcoxon signed-rank test b) the Wilcoxon rank-sum test c) the Kruskal-Wallis H test d) Spearman's rho
The Wilcoxon signed-rank test
Although similar in some ways, one difference between contingency tables and the tables used in factorial designs is a) the factorial analysis of variance tables display marginal figures, whereas contingency tables do not b) the cells in contingency tables hold frequencies, whereas the cells in factorial analysis of variance tables represent means c) contingency tables, but not factorial analysis of variance tables, rely on marginal figures d) the numbers in the cells of factorial analysis of variance tables are means for the measured variable, whereas the numbers in the cells of contingency tables represent the means for grouping variables
The cells in contingency tables hold frequencies, whereas the cells in factorial analysis of variance tables represent means
"(NColumns-1)(NRows-1)" is the formula for the degrees of freedom for a) the chi-square test for goodness of fit b) the chi-square test for independence c) the chi-square statistic estimated from a one-way analysis of variance d) the chi-square statistic estimated from a two-way analysis of variance
The chi-square test for independence
In a chi-square test of independence, the term "expected frequency" generally refers to a) the distribution of people over categories on the measured variables under the assumption of equal numbers of people in all cells b) the distribution of people over categories on one variable expected if the distribution of people over categories on the other variable is completely unrelated to it c) the examination of the spread of the grouping variable to see if it is truly an independent variable d) the population's distribution of the scores on the measured variable as estimated by the sample data
The distribution of people over categories on one variable expected if the distribution of people over categories on the other variable is completely unrelated to it
A contingency table is a table in which a) the distributions of two nominal variables are laid out so that you have the frequencies of their combinations and totals can be seen b) chi-squares for each category are displayed over each level of the predictor variable c) χ2 distributions are translated into t distributions d) χ2 distributions are translated into F distributions
The distributions of two nominal variables are laid out so that you have the frequencies of their combinations and totals can be seen
When a chi-square test is reported in a research article, which information is typically missing? a) the degrees of freedom b) the number of observed cases in each cell c) the significance of χ2 d) the expected value for each cell
The expected value for each cell
The main difference between the test for goodness of fit and the test for independence is that a) the goodness of fit test can be used only for 2 × 2 designs whereas the independence test is not limited to a particular design type b) expected frequencies are calculated for the independence test but not for the goodness of fit test c) the goodness of fit test is limited to one nominal variable whereas the independence test is not d) observed frequencies are compared to expected frequencies for the independence test but not for the goodness of fit test
The goodness of fit test is limited to one nominal variable whereas the independence test is not
The degrees of freedom for the chi-square test for goodness of fit is a) the number of categories minus one b) the mean number of individuals per category minus the number of categories c) the mean number of individuals per category minus one d) the total number of individuals minus the number of categories
The number of categories minus one
The degrees of freedom for the chi-square test for independence is a) the number of categories minus one b) the number of columns minus one multiplied by the number of rows minus one c) the total number of category levels minus one d) the number of people minus the number of cells
The number of columns minus one multiplied by the number of rows minus one
The mean and variance of rank-ordered scores depends on a) the number of groups b) the most frequent score c) the number of scores that are ranked d) the mean and variance of the untransformed scores.
The number of scores that are ranked
In a chi-square test for independence, the null hypothesis is that a) the two population variances are independent b) the two variables are independent in the population c) the means of the populations are not equal d) the means of the populations are equal
The two variables are independent in the population
When discussing the pattern in a contingency table, the word "independence" means a) the distribution of one variable varies over different levels of the other b) the variables in the table should not be compared c) the observed frequencies are larger than the expected frequencies d) there is no relationship between the variables
There is no relationship between the variables
A widely used procedure when the sample's scores do not appear to come from a normal population is to a) duplicate scores which will make the sample more normal b) sample only members of the population who will make the sample normal c) transform the sample scores d) delete the scores that make the distribution non-normal if the results are not significant
Transform the sample scores
When carrying out a chi-square test for independence, a good check on the arithmetic in figuring the expected frequencies is to make sure that a) the expected frequency of each cell is no larger than the observed frequency b) the sum of all the expected frequencies times the degrees of freedom equals the sum of all the observed frequencies c) within any one row or column, the sum of the observed frequencies and the sum of the expected frequencies are the same d) the sum of all the expected frequencies for each row equals the sum of all the observed frequencies for each column minus 1
Within any one row or column, the sum of the observed frequencies and the sum of the expected frequencies are the same
The formula for the chi-squared statistic is a) Σ[(O-E)2/E] b) [Σ(O-E)2]/E c) O/[Σ(O-E)2] d) E/[Σ(O-E)2]
Σ[(O-E)2/E]
√(χ2/N) is the formula for a) δ b) α c) Φ d) μ
Φ
The distribution that is always greater than 0 and positively skewed is the distribution for a) Z b) t c) χ2 d) U
χ2
The item below is based on the following scenario. In a third world country, 100 randomly selected people were surveyed about their socioeconomic class and religious affiliation. The results and an excerpt from this fictitious study follow: Observed (and Expected) Frequencies Excerpt: "Based on a chi-square test for independence, the working class differed from the middle class in the distribution of religious identification, χ2 (4, N = 100) = 11.73, p < .05." The phi coefficient for this study is a) √(11.732/100) = 1.17 b) √(11.73/1002) = .03 c) √(11.73/100) = .34 d) √[11.732/(100-1)] = 1.18
√(11.73/100) = .34
In a study with 100 participants, an analysis results in a χ2 of 3.15. What is the phi coefficient? a) √(3.15/1002) = .02 b) √(3.152/100) = .32 c) √[(3.15/(100-1)] = .18 d) √(3.15/100) = .18
√(3.15/100) = .18
The phi coefficient is a) always less than 0 b) √(χ2/N) c) always greater than 1 d) always less than 1
√(χ2/N)
The formula for Cramer's phi statistic is a) √(χ2/N/dfSmaller) b) √(χ2/df) c) √(χ2/N) d) √[χ2/(N)(dfSmaller)]
√[χ2/(N)(dfSmaller)]
